Moduli problems for operadic algebras

Abstract

A theorem of Pridham and Lurie provides an equivalence between formal moduli problems and Lie algebras in characteristic zero. We prove a generalization of this correspondence, relating formal moduli problems parametrized by algebras over a Koszul operad to algebras over its Koszul dual operad. In particular, when the Lie algebra associated to a deformation problem is induced from a pre-Lie structure it corresponds to a permutative formal moduli problem. As another example we obtain a correspondence between operadic formal moduli problems and augmented operads.

Major reorganization of the paper in order to increase readability. No change to main results, but some examples were added. To appear on JLMS

References in corpus (5)

• Coloured Koszul duality and strongly homotopy operads
• Pro-algebraic homotopy types
• Formal moduli problems and formal derived stacks
• Review of deformation theory II: a homotopical approach
• Localizing infinity-categories with hypercovers